Finite Group Databasebeta

← Group #272297

Character table — Group #272297

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222222444448888888888888888816161616161616161616161616161616163232
order12222244444444444222444444888888882444488888888888848
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-111111-1-11-1111-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-111-1-111
χ51111111111111111111-1-11-1-11111-1-11111-111-111-1-111-1-1-1-1-1-1-11-1
χ61111111111111111111-1-11-1-111-1-1-1-1-1-1-1-1-111-11-111-1-1-1-1-11111-11
χ71111111111111111111-1-11-1-1-1-111111111-1-1-1-1-11-1-1-1-111111-1-1-11
χ81111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1111-1
χ91111111111111-1-111-1-111-111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-111
χ101111111111111-1-111-1-111-11111-1-1111111-1-1-1-11-1-1-1111-1-11111-1-1
χ111111111111111-1-111-1-111-111-1-111-1-1-1-1-1-1-111-1-111111-11111-1-1-1-1
χ121111111111111-1-111-1-111-111-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-111-1-11111
χ131111111111111-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-1-1-1-1-11111111-1
χ141111111111111-1-111-1-1-1-1-1-1-111-1-1-1-111111-1-111-11111-111-1-1-1-1-11
χ151111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-1-1-1-111-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11-1-111-1-11-1
χ1722222222-2-2-2-2222-2-2-2-20020000000000000000002i−2i00000002i−2i00
χ1822222222-2-2-2-2222-2-2-2-2002000000000000000000−2i2i0000000−2i2i00
χ1922222222-2-2-2-22-2-2-2-22200-20000000000000000002i−2i0000000−2i2i00
χ2022222222-2-2-2-22-2-2-2-22200-2000000000000000000−2i2i00000002i−2i00
χ21222222-2-22222-200-2-2002-202-222002200000000-200000-200000000
χ22222222-2-22222-200-2-2002-202-2-2-200-2-200000000200000200000000
χ23222222-2-22222-200-2-200-220-222200-2-200000000-200000200000000
χ24222222-2-22222-200-2-200-220-22-2-2002200000000200000-200000000
χ252222-2-22222-2-2-222-222-200-20000220022-2-200000-20000000000000
χ262222-2-22222-2-2-222-222-200-20000-2-200-2-2220000020000000000000
χ272222-2-22222-2-2-2-2-2-22-2200200002200-2-22200000-20000000000000
χ282222-2-22222-2-2-2-2-2-22-220020000-2-20022-2-20000020000000000000
χ292222-2-222-2-222-2222-2-2222-2-2-20000000000-2002000000000000000
χ302222-2-222-2-222-2222-2-22-2-2-2220000000000200-2000000000000000
χ312222-2-222-2-222-2-2-22-22-2222-2-20000000000200-2000000000000000
χ322222-2-222-2-222-2-2-22-22-2-2-22220000000000-2002000000000000000
χ332222-2-2-2-2-2-222200-22002-20-22000000000002-2000000002-2000000
χ342222-2-2-2-2-2-222200-22002-20-2200000000000-2200000000-22000000
χ352222-2-2-2-2-2-222200-2200-2202-2000000000002-200000000-22000000
χ362222-2-2-2-2-2-222200-2200-2202-200000000000-22000000002-2000000
χ37444444-4-4-4-4-4-4-40044000000000000000000000000000000000000
χ384444-4-4-4-444-4-44004-4000000000000000000000000000000000000
χ3944-4-400-44000004i−4i0000000000022−22002i2−2i2000000000000000000000
χ4044-4-400-44000004i−4i00000000000−222200−2i22i2000000000000000000000
χ4144-4-400-4400000−4i4i0000000000022−2200−2i22i2000000000000000000000
χ4244-4-400-4400000−4i4i00000000000−2222002i2−2i2000000000000000000000
χ434-44-44-4004-44-40000000000000000000000000000002i2−2i2000000000
χ444-44-44-4004-44-4000000000000000000000000000000−2i22i2000000000
χ454-44-44-400-44-4400000000000000004i−4i00000000000000000000000
χ464-44-44-400-44-440000000000000000−4i4i00000000000000000000000
χ474-44-4-44004-4-440000000000004i−4i000000000000000000000000000
χ484-44-4-44004-4-44000000000000−4i4i000000000000000000000000000
χ494-44-4-4400-444-4000000000000000000000000000000000002i2−2i20000
χ504-44-4-4400-444-400000000000000000000000000000000000−2i22i20000
χ5188-8-8008-8000000000000000000000000000000000000000000000
χ528-8-8800000000000000000000000000004i−4i0000000000000000000
χ538-8-880000000000000000000000000000−4i4i0000000000000000000

Here i is the imaginary unit (i² = −1).